Question 897529
1,2,3,14
4,-1,-1,-1
7,5,1,20


add  down (-4) *row 1 to row 2
1,2,3,14
0,-9,-13,-57
7,5,1,20

add  down (-7) *row 1 to row 3
1,2,3,14
0,-9,-13,-57
0,-9,-20,-78

divide row 2 by -9
1,2,3,14
0,1,-13/-9,-57/-9
0,-9,-20,-78

add  down (9) *row 2 to row 3
1,2,3,14
0,1,13/9,19/3
0,0,-7,-21

divide row 3 by -7
1,2,3,14
0,1,13/9,19/3
0,0,1,3

We now have the value for the last variable.
We will work our way up and get the other solutions.

add up  (-13/9) *row 3 to row 2
1,2,3,14
0,1,0,2
0,0,1,3

add up  (-3) *row 3 to row 1
1,2,0,5
0,1,0,2
0,0,1,3

add up  (-2) *row 2 to row 1
1,0,0,1
0,1,0,2
0,0,1,3


1,0,0,1
0,1,0,2
0,0,1,3
"1","2","3"
(1,2,3)